Efficient evaluation of three-phase coexistence lines

The Gibbs-Duhem integration method is a means for evaluating phase diagrams by molecular simulation. Starting from a state of known phase coexistence, one applies the Clapeyron equation to trace out subsequent points on the saturation line. Each simulation yields a coexistence state, and particle exchanges are not invoked to insure equality of fugacities. We describe and demonstrate here the extension of this method to three-phase coexistence, namely, among a solid, a liquid, and a gas. In one application, we compute the saturation pressure and temperature as a function of composition (more accurately, as a function of fugacity fraction) for six Lennard-Jones two-component mixtures. In a second study, we traverse a mutation pathway; that is, we evaluate three-phase equilibria as a function of the intermolecular potential. In particular, we define a path that transforms the Lennard-Jones model into a square well, and thus in our calculations we quantify the effect of the shape of the repulsive and attractive portions of the potential on the triple point. In the end we have what is, to our knowledge, the First estimate of a state of solid-fluid coexistence for a square well model. In both applications we assume that the fee crystal structure represents the thermodynamically stable solid phase.